Evaluation of Non-Uniform B-spline Surfaces on GPUs

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In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform B-spline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We show that efficient computation of positions and normal vectors for B-spline surfaces can be done on GPUs by applying these ideas. Our algorithm computes an exact position, a derivative and a curvature per fragment. We demonstrate that this achieves high-quality surface rendering. We also discuss about the extension to NURBS and trimmed surfaces.

Papers

  • Takashi Kanai: “Fragment-based Evaluation of Non-Uniform B-spline Surfaces on GPUs”, Computer-Aided Design and Applications (Proc. CAD’07 Conference, Honolulu, Hawaii, 25-29 June, 2007), Vol.4, Nos.1-4, pp.287-294, 2007.
    [paper (Adobe PDF) (829KB)]